Question

Encontre o valor de x em função de a.

$\frac{35a {}^{2} }{4} = (x + a) \times x$
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Answer 1

$\frac{35a {}^{2} }{4} = (x + a) \times x \\ {x}^{2} + ax = \frac{ 35{a}^{2} }{4}$

${x}^{2} + ax + \frac{ {a}^{2} }{4} = \frac{35 {a}^{2} }{4} + \frac{ {a}^{2} }{4} \\ {(x + \frac{a}{2} )}^{2} = \frac{36 {a}^{2} }{4}$

${(x + \frac{a}{2} )}^{2} = 9 {a}^{2} \\ x + \frac{a}{2} = \sqrt{9 {a}^{2} } \\ x + \frac{a}{2} = 3a$

$x = 3a - \frac{a}{2} \\ x = \frac{6a - a}{2} \\ x = \frac{5a}{2}$